Related papers: The p-AAA algorithm for data driven modeling of pa…
Bistable tape spring booms are used on spacecraft for their ability to self-deploy using stored strain energy. However, their uncontrolled deployment can induce mechanical shocks that are variable as a function of material properties and…
In this paper, a systematic approach is developed to embed the dynamical description of a nonlinear system into a linear parameter-varying (LPV) system representation. Initially, the nonlinear functions in the model representation are…
Additive models form a widely popular class of regression models which represent the relation between covariates and response variables as the sum of low-dimensional transfer functions. Besides flexibility and accuracy, a key benefit of…
In this paper we present a data driven approach for approximating dynamical systems. A dynamics is approximated using basis functions, which are derived from maximization of the information-theoretic entropy, and can be generated directly…
Autonomous Aerial Manipulators (AAMs) are inherently coupled, nonlinear systems that exhibit nonstationary and multiscale residual dynamics, particularly during manipulator reconfiguration and abrupt payload variations. Conventional…
In this paper an autonomous analytical system of ordinary differential equations is considered. For an asymptotically stable steady state x0 of the system a gradual approximation of the domain of attraction DA is presented in the case when…
In many specific scenarios, accurate and effective system identification is a commonly encountered challenge in the model predictive control (MPC) formulation. As a consequence, the overall system performance could be significantly weakened…
Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling…
Multivariate functional data from a complex system are naturally high-dimensional and have complex cross-correlation structure. The complexity of data structure can be observed as that (1) some functions are strongly correlated with similar…
A method for approximating continuous functions $\mathbb{Z}_{p}^{n}\rightarrow\mathbb{Z}_{p}$ by a linear superposition of continuous functions $\mathbb{Z}_{p}\rightarrow\mathbb{Z}_{p}$ is presented and a polynomial regression model is…
We consider the Adaptive Antoulas-Anderson (AAA) rational interpolation algorithm recently developed by Trefethen and co-authors, which can be viewed as a type of moment-matching technique for system realization and approximation. We…
We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix…
Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…
In this document, some novel theoretical and computational techniques for constrained approximation of data-driven systems, are presented. The motivation for the development of these techniques came from structure-preserving matrix…
We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by…
This paper presents a novel theoretical framework for reducing the computational complexity of multi-model adaptive control/estimation systems through systematic transformation to controllable canonical form. While traditional multi-model…
Particle dynamics and multi-agent systems provide accurate dynamical models for studying and forecasting the behavior of complex interacting systems. They often take the form of a high-dimensional system of differential equations…
We propose a probabilistic semantic filtering framework in which parameters of a dynamical system are inferred and associated with a closed set of semantic classes in a map. We extend existing methods to a multi-parameter setting using a…
This paper introduces a novel algorithmic solution for the approximation of a given multivariate function by a nomographic function that is composed of a one-dimensional continuous and monotone outer function and a sum of univariate…
The need for multimodal data integration arises naturally when multiple complementary sets of features are measured on the same sample. Under a dependent multifactor model, we develop a fully data-driven orchestrated approximate message…